Laundry treating appliances, such as clothes washers, can include a perforate rotatable drum or basket positioned within an imperforate tub to be rotated by a motor. The drum can at least partially define a treating chamber in which a laundry load can be received for treatment according to a selected cycle of operation. The drum can also be rotationally coupled with a balance ring containing a set of masses. During at least one phase of a selected cycle, the motor operably spins the drum and laundry load about a rotational axis at a predetermined high speed, sufficient to centrifugally move and hold laundry load items against the perimeter of the treating chamber, causing liquid to be removed from the laundry load. The speed at which the clothes cease to move with respect to the drum but are held in contact with it can be referred to as the “satellization” speed. During the at least one phase of high speed rotation, the set of masses can traverse the balance ring to generate a counterbalance force to reduce/eliminate an imbalance of the laundry load.